3 Why Use SDP? 5 3.1 Tractable Relaxations of Max-Cut . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Simple Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Trust Region Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.3 Box Constraint Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.4 Eigenvalue Bound . . . . . . . . . . . . ...

One of the most remarkable basis of the gravity data inversion is the recognition of sharp boundaries between an ore body and its host rocks during the interpretation step. Therefore, in this work, it is attempted to develop an inversion approach to determine a 3D density distribution that produces a given gravity anomaly. The subsurface model consists of a 3D rectangular prisms of known sizes ...

This paper considers the problem of finding and verifying feasible points for constraint satisfaction problems, including those with uncertain coefficients. The main part is devoted to the problem of finding a narrow box around an approximately feasible solution for which it can be rigorously and automatically proved that it contains a feasible solution. Some examples demonstrate difficulties w...

1 ABSTRACT A constraint satisfaction problem (CSP) may be overcon-strained and not admit a complete solution. Optimal solutions to such partial constraint satisfaction problems (PCSPs), in which a maximum number of constraints are satissed, can be found using branch and bound variants of CSP algorithms. Earlier work has shown how information gained through local consistency checking during prep...

A constraint satisfaction problem (CSP) requires a value, selected from a given ®nite domain, to be assigned to each variable in the problem, so that all constraints relating the variables are satis®ed. Many combinatorial problems in operational research, such as scheduling and timetabling, can be formulated as CSPs. Researchers in arti®cial intelligence (AI) usually adopt a constraint satisfac...

We introduce a novel global constraint for the total weighted completion time of activities on a single unary capacity resource. For propagating the constraint, an O(n) algorithm is proposed, which makes use of the preemptive mean busy time relaxation of the scheduling problem. The solution to this problem is used to test if an activity can start at each start time in its domain in solutions th...

This paper unifies the work on multiple reinsurers, distortion risk measures, premium budgets, and heterogeneous beliefs. An insurer minimizes a measure, while seeking reinsurance with finitely many reinsurers. The reinsurers use principles, they are allowed to have beliefs regarding underlying probability distribution. We provide characterization of optimal indemnities, we show that layer-insu...

This paper develops a new generalized-branching technique called “explicitconstraint branching” (ECB) to improve the performance of branch-andbound algorithms for solving mixed-integer programs (MIPs). ECB adds structure to a MIP, in the form of auxiliary constraints and auxiliary integer variables, to allow branching on groups of (original) integer variables that would not otherwise be possibl...

Constraints satisfaction problems are often used for modeling and solving problems in an environment which is subject to changes. When some of the constraints are changed after a solution was obtained it is often desired to search for a solution to the derived problem where the solution to the changed problem is as similar as possible to the previous (e.g., current) solution. This requirement i...